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(198
The Arc Do to be of 12'33",3.  But the Angle CP [[underlined]] o [[/underlined]], would be of 8'32",1.  The Difference O [[underlined]] o [[/underlined]], is of 4'1", 1 1/2, and by consequence almost the very same as O [[underlined]] o [[/underlined]]. And the Error in Longitude would be found almost the same as before.
6. As to the Error in Latitude, it can amount at most, only to the Arc MF of 2'12", taking 1'6" for the horizontal Refraction of Light in the. Atmosphere of the Moon.  And you may take the following Rule.
7. Let a Star describe any given Parallel D [[underlined]] 0 [[/underlined]] O, cutting the Circle F [[underlined]] ƒ0 [[/underlined]] N in [[underlined]] O [[/underlined]]. Draw the Line C [[underlined]] Oz [[/underlined]], which cuts the Limb MEL in [[underlined]] z [[/underlined]].  And in the Triangle PC [[underlined]] 0 [[/underlined]],  the three Sides being given, calculate the Angle PC [[underlined]] 0 [[/underlined]] or PC [[underlined]] z [[/underlined]]. Then in the Triangle PC [[underlined]] z [[/underlined]], the Sides PC and C [[underlined]] z [[/underlined]] and the Angle PC [[underlined]] z [[/underlined]] being given, calculate the Basis  P [[underlined]] z [[/underlined]].  And since the Star coming to O emerges in [[underlined]] z [[/underlined]], and the Astronomical Calculation makes it more truly to emerge in O; it follows that y [[superscript]] e [[/superscript]] Observation shews the Emersion, as if the Parallel of the Star passed thro' [[underlined]] z [[/underlined]]; and by consequence as if the Moon's Declination PC, or the Situation of her Center C was changed, till the Point [[underlined]] z [[/underlined]] of her Limb was brought, by a Circle Parallel to MP, to the Parallel D [[underlined]] 0 [[/underlined]] O.  And thus you will find how much the Refraction alters your Latitude, or the apparent Distance of the Center of the Moon from the Pole: For these two Quantities depend upon one another.
Gent. Mag. 1738. p. 265.
Worcester, May 15. 1738.        
N. Facio, [[underlined]] Duillier [[/underlined]].
Subject Continued on p. 208.        

Transcription Notes:
edited mainly for spacing. -megshu